Global regularity of 2D almost resistive MHD equations

Global regularity of 2D almost resistive MHD equations

Whether or not the solution to 2D resistive MHD equations is globally smooth remains open. This paper establishes the global regularity of solutions to the 2D almost resistive MHD equations, which require the dissipative operators L weaker than any power of the fractional Laplacian by taking advanta...

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Veröffentlicht in:Nonlinear analysis: real world applications 2018-06, Vol.41, p.53-65
Hauptverfasser: Yuan, Baoquan, Zhao, Jiefeng
Format: Artikel
Sprache:eng
Schlagworte:
Almost resistive MHD equations
Cauchy problems
Fluid mechanics
Global regularity
Laplace transforms
Magnetohydrodynamics
Mathematical analysis
Nonlinear maximal principles
Regularity
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Zusammenfassung:Whether or not the solution to 2D resistive MHD equations is globally smooth remains open. This paper establishes the global regularity of solutions to the 2D almost resistive MHD equations, which require the dissipative operators L weaker than any power of the fractional Laplacian by taking advantage of nonlinear maximum principles. The result is an improvement of the one of Fan et al. (2014) which ask for α>0,β=1.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2017.10.006